A		C	D
11		211	211
12		125	121
7		179	185
12		225	222
11		161	157
15		170	174
6		191	184
16		195	194
12		135	133
13		162	165
9
14
11
10
8
15
14
13
9
6
8
12
14
16
11

1. The mean of the distribution of potato sack weights is 80 lbswith a standard deviation of 4 lbs. Assume that the distributionapproximates a Bell curve.

1. Use the z-table calculator and find the weight which is the70th percentile. Use value from an are (Show a screen shot for youranswer.)
2. What is the z-score for a weight of 75 lbs? z-score =(x-µ)/σ
3. Suppose you pick a single sack at random. What is theprobability that the weight will be between 85 and 100 lbs? Usearea from a value. (Show a screen shot for your answer.)

Use the central limit theorem to thefollowing questions.

1. Suppose you pick a group of 9 sacks instea What would be thestandard deviation of the sample’s (group’s) average using thecentral limit theorem? (i.e. σ_xbar = σ/)
2. What is the probability that a group of 9 sacks will have anaverage weight between 90 and 100 lbs? Use the z-table calculatorwith “area from a value”. (Show a screen shot for youranswer.)

1. Use Column A.

We want to test to see whether thedata taken from 25 test experiments is consistent with the meanequal to 10.3 (µ = 10.3), or is more consistent with the meangreater than 10.3 (µ > 10.3).

Use Summary 5b, Table 2, Column 1.

1. What is the null hypothesis H_o for our test?
2. What is the alternative hypothesis H_a?
3. What type of tail test will we use? (left tail, right tail, ortwo tails)?
4. What is the mean of the sample xbar?
5. What is the standard deviation of the sample s?
6. What is the size of the sample n?
7. We going to use a t-statistic. Explain why we are not going touse a z-statistic.
8. Calculate the t-statistic using xbar, µ, n, and s.
9. How many degrees of freedom does this data set have?
10. Use the t-distribution calculator to compute a p-value. Includea screen shot of your answer.
11. We want a 99% confidence level. Based on your value of p,should we accept or reject the null hypothesis?
12. What if we want a 95% confidence level? Based on your value ofp, should we accept or reject the null hypothesis?

1. Use Columns C and D for this question.

You are measuring weight loss usingthe same set of people at different times C and D. You want to knowwhether there is any difference in the weight between the start ofthe diet and the end of the diet. Column C gives the weight at thebeginning of diet time. Column D gives the weight for the SAMEperson at the end of the diet time. Since there is data for thesame person at different times, we will test whether µ(C-D) <= 0or µ(C-D) > 0 (meaning the diet did cause weight loss) since wehave correlated data (matched pairs).

Use Summary 5b, Table 2, Column 1

1. Make a new series of data samples by letting E = C – D. Listyour new series of 10 numbers.
2. What is the null hypothesis H₀ ?
3. What is the alternative hypothesis H_a ?
4. What type of tail test are we going to use? (left tail, righttail, two tail)
5. What is the mean xbar of this new sample?
6. What is the standard deviation of the sample s?
7. What is the size of the sample n?
8. How many degrees of freedom does this data set have?
9. What is the t-statistic for this sample?
10. Use the t-distribution calculator to compute a p-value. Show ascreen shot of your answer.
11. Based on this value of p and using a 90% confidence level, isthere a systematic difference in the weight changes between thestart and stop time of the diet? Should we accept or reject thenull hypothesis?